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Paper detail

A non-expanding transport distance for some structured equations

Structured equations are a standard modeling tool in mathematical biology. They areintegro-differential equations where the unknown depends on one or several variables, representing the state or phenotype of individuals. A large literature has been devoted to many aspects of these equations and in particular to the study of measure solutions.Here we introduce a transport distance closely related to the Monge-Kantorovich distance,which appears to be non-expanding for several (mainly linear) examples of structured equations.

preprint2021arXivOpen access
Nicolas FournierBenoît Perthame
math.AP
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Nicolas FournierBenoît Perthame

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